This is part of an assignment. I feel like this is a really trivial question or I'm missing some key idea. I'm asked whether exchanging the rows affects a matrix game. I believe it doesn't because the linear combinations of either "player" in a 1 vs 1 matrix game isn't dependent on the ordering of the rows/choices.
2026-05-04 19:21:27.1777922487
Does exchanging the rows or columns of a matrix game affect the outcome?
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All you're doing by exchanging rows or columns is changing the labels used to identify the pure strategies of the row or column player respectively.
The game itself is essentially unchanged.